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gmp: Determine missing RSA private key parameters

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We only need n, e, and d.  The parameters for the Chinese remainder
algorithm and even p and q can be determined from these.
This commit is contained in:
Tobias Brunner 2017-09-22 17:49:00 +02:00
parent 03eda5a822
commit bd4df68a7b
1 changed files with 109 additions and 4 deletions
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113
src/libstrongswan/plugins/gmp/gmp_rsa_private_key.c
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@ -1,4 +1,5 @@
/*
* Copyright (C) 2017 Tobias Brunner
* Copyright (C) 2005 Jan Hutter
* Copyright (C) 2005-2009 Martin Willi
* Copyright (C) 2012 Andreas Steffen
@ -806,6 +807,82 @@ gmp_rsa_private_key_t *gmp_rsa_private_key_gen(key_type_t type, va_list args)
return &this->public;
}
/**
* Recover the primes from n, e and d using the algorithm described in
* Appendix C of NIST SP 800-56B.
*/
static bool calculate_pq(private_gmp_rsa_private_key_t *this)
{
gmp_randstate_t rstate;
mpz_t k, r, g, y, n1, x;
int i, t, j;
bool success = FALSE;
gmp_randinit_default(rstate);
mpz_inits(k, r, g, y, n1, x, NULL);
/* k = (d * e) - 1 */
mpz_mul(k, *this->d, this->e);
mpz_sub_ui(k, k, 1);
if (mpz_odd_p(k))
{
goto error;
}
/* k = 2^t * r, where r is the largest odd integer dividing k, and t >= 1 */
mpz_set(r, k);
for (t = 0; !mpz_odd_p(r); t++)
{ /* r = r/2 */
mpz_divexact_ui(r, r, 2);
}
/* we need n-1 below */
mpz_sub_ui(n1, this->n, 1);
for (i = 0; i < 100; i++)
{ /* generate random integer g in [0, n-1] */
mpz_urandomm(g, rstate, this->n);
/* y = g^r mod n */
mpz_powm_sec(y, g, r, this->n);
/* try again if y == 1 or y == n-1 */
if (mpz_cmp_ui(y, 1) == 0 || mpz_cmp(y, n1) == 0)
{
continue;
}
for (j = 0; j < t; j++)
{ /* x = y^2 mod n */
mpz_powm_ui(x, y, 2, this->n);
/* stop if x == 1 */
if (mpz_cmp_ui(x, 1) == 0)
{
goto done;
}
/* retry with new g if x = n-1 */
if (mpz_cmp(x, n1) == 0)
{
break;
}
/* y = x */
mpz_set(y, x);
}
}
goto error;
done:
/* p = gcd(y-1, n) */
mpz_sub_ui(y, y, 1);
mpz_gcd(this->p, y, this->n);
/* q = n/p */
mpz_divexact(this->q, this->n, this->p);
success = TRUE;
error:
mpz_clear_sensitive(k);
mpz_clear_sensitive(r);
mpz_clear_sensitive(g);
mpz_clear_sensitive(y);
mpz_clear_sensitive(x);
mpz_clear(n1);
gmp_randclear(rstate);
return success;
}
/**
* See header.
*/
@ -868,9 +945,30 @@ gmp_rsa_private_key_t *gmp_rsa_private_key_load(key_type_t type, va_list args)
mpz_import(this->n, n.len, 1, 1, 1, 0, n.ptr);
mpz_import(this->e, e.len, 1, 1, 1, 0, e.ptr);
mpz_import(*this->d, d.len, 1, 1, 1, 0, d.ptr);
mpz_import(this->p, p.len, 1, 1, 1, 0, p.ptr);
mpz_import(this->q, q.len, 1, 1, 1, 0, q.ptr);
mpz_import(this->coeff, coeff.len, 1, 1, 1, 0, coeff.ptr);
if (p.len)
{
mpz_import(this->p, p.len, 1, 1, 1, 0, p.ptr);
}
if (q.len)
{
mpz_import(this->q, q.len, 1, 1, 1, 0, q.ptr);
}
if (!p.len && !q.len)
{ /* p and q missing in key, recalculate from n, e and d */
if (!calculate_pq(this))
{
destroy(this);
return NULL;
}
}
else if (!p.len)
{ /* p missing in key, recalculate: p = n / q */
mpz_divexact(this->p, this->n, this->q);
}
else if (!q.len)
{ /* q missing in key, recalculate: q = n / p */
mpz_divexact(this->q, this->n, this->p);
}
if (!exp1.len)
{ /* exp1 missing in key, recalculate: exp1 = d mod (p-1) */
mpz_sub_ui(this->exp1, this->p, 1);
@ -889,6 +987,14 @@ gmp_rsa_private_key_t *gmp_rsa_private_key_load(key_type_t type, va_list args)
{
mpz_import(this->exp2, exp2.len, 1, 1, 1, 0, exp2.ptr);
}
if (!coeff.len)
{ /* coeff missing in key, recalculate: coeff = q^-1 mod p */
mpz_invert(this->coeff, this->q, this->p);
}
else
{
mpz_import(this->coeff, coeff.len, 1, 1, 1, 0, coeff.ptr);
}
this->k = (mpz_sizeinbase(this->n, 2) + 7) / BITS_PER_BYTE;
if (check(this) != SUCCESS)
{
@ -897,4 +1003,3 @@ gmp_rsa_private_key_t *gmp_rsa_private_key_load(key_type_t type, va_list args)
}
return &this->public;
}